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Abstract
This paper presents a beam control system for a graphene-based phased array antenna (PAA) using the proposed radio-over-fiber (RoF) in the THz and sub-THz bands. The generated pulses are modulated by the Mach-Zehnder modulator (MZM) and, by using the special design of the fiber under modulation instability (MI), can be amplified at the sideband of the carrier. Finally, changing the length of the compensating fiber in the bit-control system makes it possible to control the PAA beam pattern. Improving the bias voltage (Vπ) of the MZM, simplicity of the RoF system structure, and increasing the spontaneous gain caused by the MI phenomenon are the advantages of the proposed system. Therefore, it is an acceptable candidate for the beam control applications system. Also, the patch antenna is based on graphene and has a new structure. This antenna consists of radiation patches in an octagonal shape and a microstrip feed line. The antenna operates with appropriate radiation features, with gains of 12 dB and returns losses of less than -10 dB at 700 GHz bandwidth. All simulations are performed using the CST Microwave Studio and the Optiwave software.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
An expansion in the capacity of wireless networks for high-speed radio communications is in high demand in the modern day. Due to their wide range of potential bandwidths, terahertz (THz) waves, which extend in frequency from 0.3 to 10 THz, have recently attracted much attention for broadband wireless communications [1]. Therefore, perfect connectivity between the optical fiber and THz radio will be highly desired for decreasing system complexity. radio-over-fiber (RoF) technology is a potential option for implementing efficient connectivity [2]. Furthermore, this method makes it simple to combine wireless THz transmission with high-capacity optical fiber transmission utilizing the RoF transmitter at configurable frequency [3].
Free space path loss, which grows as the square of the frequency, must first be corrected for utilizing directional transmitters like high-gain directional phased arrays. On the other hand, atmospheric absorption caused by water vapor becomes a challenge [4]. Using the physical phenomena of modulation instability (MI), in the fiber optic not only makes it possible to transmit the optical signal without any attenuation but also creates spontaneous gain to save input power consumption.
MI is a nonlinear phenomenon that includes the interaction of dispersion, nonlinearity, and diffraction in the presence of a nonlinear medium. At the output of fiber under MI, the exponential expansion of the spectral sidebands of the carrier is expected. In this case, rapid fluctuations appear as modulated pulse trains when the carrier wave (CW) is laser optical [5].
RoF technology allows efficient media conversion between radio and optical signals in a fiber-optic network. The wireless link reduces the difference in data rates between wireline and wireless. As a result, for the 5G era and beyond, mobile backhauling and front-hauling using RoF with high-capacity fiber-wireless links operating at the mm-wave and THz band is being considered [6,7]. In addition, there are non-telecom applications for the last-mile access network where optical network deployment is challenging or uneconomical [8,9]. Creating mm-wave and THz waves with low-phase noise is essential in each application. Since the THz region is between the microwave and infrared spectrums, electronics and photonics, enable the creation of mm-wave, and THz signals [6,7]. Also, there were limitations to generating THz input pulses in the past. It is currently possible to create these pulses in the THz frequency band. In this way, generating pulses at a frequency of 700 GHz is shown in [10,11].
In a conventional RoF system, these pulses can be modulated to transmit them over long distances through fiber optics with very low loss for telecommunication applications. Mach-Zehnder modulator (MZM) is one of the most widely used modulators in RoF systems. This modulator had many challenges, including a high bias voltage at high frequencies and limited bandwidth. Several articles have recently been published describing the MZM with a terahertz bandwidth. In [4], the MZM with a bandwidth of 500 GHz was proposed; in [12], it was demonstrated that the MZM could also operate beyond 800 GHz. As a result, the frequency range is adaptable to our proposed system.
In the THz systems, many antenna units would be required to cover broad areas for detecting and scanning accurately to achieve more data and information in the study environments. A particularly promising research field is using the graphene-enabled antenna in wireless communications. Graphene has exceptional properties, such as its extremely high electrical conductivity, half-integer quantum hall effect, ballistic electron transport, optoelectronic applications, superior crystal quality, ultra high-elastic flexibility, and high mechanical strength, gained significant attention in recent years [13,14].
Graphene-based phased array antenna (PAA) is one of the most popular radiating elements in the sub-THz and THz bands. There are many designs and structures of patch-array antenna-based graphene with acceptable high gain and low return loss, such as ultra-wideband metamaterial absorber [15], in medicine and biology [16], tunable sensors [17], and useful devices for high-tech systems like transistors [18].
Recently, different sub-THz antenna arrays based on slots [19] or printed dipoles [20] have been studied for THz spectroscopy; nevertheless, the radiation characteristics of these antennas are constrained for practical use. As a result, there is a need for antennas operating at these frequencies that have better radiation gain and efficiency characteristics.
Optical beamforming for PAAs has received a lot of attention in recent years. The microwave signal is modulated into an optical carrier and transmitted via various optical pathways to realize different true time delay values [21]. Recently, the researchers operated methods for manipulating beam shape such as near-field transformation [22], using compact frequency selective surface (FSS) [23], and various optimization algorithms like artificial intelligence (AI) [24]. To lower the costs and increase simplicity, different methods such as including wavelength division multiplexing [25], and switchable waveguide delay lines [26] can be used.
This paper proposes a novel method for exploiting the MI phenomenon in fiber optics for sub-THz and THz applications. In this case, THz pulses are amplified at the high-frequency spectral range of the carrier sideband. The MI gain occurs spontaneously in the fiber, significantly reduces input power, improves bias voltage ($V_{\pi }$) of the MZM and simplifies the RoF structure (by eliminating extra pumps). In addition to improving the performance of graphene-based PAA by applying MI gain to each radiating element, the proposed method also allows the beam angle of PAA to be tuned through programmable controls. It is important to note that the design of the graphene-based PAA is innovative. The octagonal antenna has the benefits of the square and circular patch antennas simultaneously, which offers better gain than the standard patch [27]. This antenna geometry is helpful for its acceptable features in medical, wireless communication, and high-tech technology.
The rest of the paper is organized as follows: The proposed RoF structure for wireless communication in THz frequency bands is presented in section II. Section III explains the fiber performance under MI phenomena with its improvement of the $V_{\pi }$ and the system’s gain. Section IV presents the new octagonal graphene-based patch array antenna design and the simulation results. Section V discusses the suggested method for PAA’s beam control. Finally, the conclusions are summarized in section VI.
2. THz radio over fiber structure
RoF technology is an efficient method that reduces signal loss and increases wireless communication range. Also, the signal transmission in the THz band based on the RoF system is essential for high-frequency communication applications.
Figure 1 shows the schematic of the proposed RoF system. It consists of generated modulated THz pulses using MZM and transmitted through fiber optics under MI phenomena. After that, this signal is demodulated with a photodetector for a graphene-based array antenna. Moreover, the programmable bit-control system based on the fiber length is utilized to create the desired beam for the PAA.
Fig. 1. Proposed structure of THz RoF system for long-distance communication for graphene-based phased array antenna applications.
The beam of the PAA can be controlled by tuning the time delay of the exciting signal for radiating elements. According to Eq. (1), this time delay can be created by changing the fiber length ($L$).
where $D$ and $\Delta \lambda$ represent the dispersion of the fiber and the difference between adjacent pulse wavelengths, respectively.The minimum and maximum fiber lengths used in the control system are $L$ and $7L$. To have the minimum time delay, we proposed the equation $|D_1 L_1| = |D_2 L_2|$, in which $D_1$ and $L_1$ are parameters of the fiber under MI. $D_2$ and $L_2$ are the parameters of the fiber which are used in the control system.
Therefore, the minimum time delay can be achieved by selecting the fiber with positive group velocity dispersion in the control system.
Afterwards, signals are demodulated by photodetectors and used for the antenna. It is important to note that amplifying the signal can reduce the effect of noises caused by the photodetector (such as shot noise and thermal noise).
Consequently, this proposed RoF system is more economical and simple by avoiding using another structure like an external pump for amplifying the signal level.
3. Modulation instability phenomenon
Many nonlinearities can indeed produce modulation instability. In fiber optics, they are usually brought on by an optical fiber’s Kerr nonlinearity in combination with abnormal chromatic dispersion. Therefore, amplifying the sidebands in the optical spectrum causes the optical power to fluctuate more frequently [28].
In this case, the one-dimensional propagation of light in a single-mode fiber with a nonlinear coefficient $\gamma$ and an anomalous group velocity dispersion ($\beta _2 < 0$), the propagation can be described with the nonlinear Schrödinger equation as follows:
The continuous wave for the previous equation has a soliton form when the laser’s response is lossless.
In the power of the laser, by considering the stability condition for the steady-state against small perturbation, the sideband gain is achieved by:
where the $G_{MI}$ is the modulation instability gain, $\Omega$ is the frequency ,and $\Omega _c=\sqrt {\frac {4\gamma P_0}{|\beta _2|}}$ that $P_0$ is carrier power. The nonlinear fiber with a specified design and under modulation instability amplifies a particular spectral range of the carrier sideband by nonlinear frequency variation on the laser wave under effect. This amplification can be applied and employed without a separate pump using only the anomalous fiber [29].Figure 2 shows the sideband amplification for different fiber lengths with a -78 dBm constant input power. The group velocity dispersion and the nonlinear index of refraction of fiber are $\beta _2$=-0.0059 $ps^2/km$ and $n_2$= $10^{-20}$ $m^{2}.W^{-1}$, respectively. It is important to note that all simulations of the RoF system are performed using Optiwave software.
The gain at the sideband carrier increases by raising the length of the fiber too. The gain per fiber lengths of 15 km, 30 km, 45 km, and 60 km are 6.6 dB, 15 dB, 23.4 dB, and 32 dB, respectively. Because of the atmospheric attenuation, the signal quality and power of the electromagnetic (EM) signal transfer decrease significantly. Therefore, obtaining a high gain in this situation is vital for communication networks by reducing the value of path loss. In this proposed method, the MI gain is caused by using anomalous fibers and gives great amplifying that decreases the cost of the RoF system by eliminating other amplifiers. The MI phenomenon raises the gain spontaneously in the sideband and improves the efficiency of the MZM. Increasing the $V_{\pi }$ regarding raising the frequency is one of the critical challenges in designing broadband travelling-wave modulators like MZ that have approved performance. However, this ratio is inverse in electrical devices like CMOS [30]. One of the advantages of the proposed structure is that by helping MI gain in the sideband of the carrier, $V_\pi$ of MZM improved as follows:
$L_{Dep}^{1/2}$ <1 is the consumption factor for the power carrier. The effective half wave voltage $V_{\pi,eff}$ is decreased by utilizing the $G_{MI}$ in the sideband, which helps to domain the $V_{\pi }$ challenge.
By adopting a fiber with constant group velocity dispersion and under MI, the maximum gain ($G_{max}$=$\frac {\Omega _c^2|B_2|}{2}$) occurs at frequency $\Omega _{max}$=$\pm \frac {\Omega _c}{\sqrt 2}$ and respect to Eq. (4) is :
Although in transmitting and receiving communication applications, the modulator’s performance is improved by raising the gain, which reduces the $V_{\pi,eff}$ and clarifies the detection of the received signal. It is necessary to remember that the fiber operating under MI will inherently amplify pulses without the assistance of an additional pump or amplifier. Therefore, improving $V_{\pi }$ with MI is possible.
By using fiber with lengths of 15 km, 30 km, 45 km, and 60 km, $V_{\pi,eff}$ reach about $0.46V_{\pi }$, $0.17V_{\pi }$, $0.06V_{\pi }$, and $0.025V_{\pi }$ respectively.
4. Structure of the proposed PAA-based graphene and results
Graphene is one of the most recent materials discoveries, which has received much attention due to its unique physical and chemical properties, especially in THz communications [17,31,32].
It is important to note that the applied voltage configures the electric carrier of the graphene. One of graphene’s main characteristics is its extremely high electrical conductivity, which is evaluated using the Kubo formula and divided into two categories: $\sigma _{GR}(\omega,\mu,$T$, \tau )$ = $\sigma _{inter}$ + $\sigma _{intra}$ (Eqs. (8), and, (9)) [33].
Without considering the effect of the magnetic field, this formula could be represented as:
In this formula, $\mu$ is the chemical potential, $\omega$ is the radian frequency, $T$ is the environment’s temperature, and $\tau$ is the relaxation time. Also, the Fermi distribution is $f_d(\varepsilon ) = (e^{(\frac {\varepsilon -\mu _c}{K_BT})}+1)^{-1}$, where $e$ is electron charge, $h$ is reduced Planck’s constant and $K$ is Boltzmann’s constant. In addition, the relationship between $\mu _c$ and $n_s$ (carrier density) is expressed as follows [33]:
The real part is involved in the absorption and dissipation of energy due to the presence of intra-band electrons. In addition, the $\mu _c$ of the graphene related to $n_s$ is as follows.
It is essential to note that due to the $\sigma _{gi}$ and $\sigma _{gr}$, the appropriate relative graphene is given by:
where $s$ is the thickness of graphene layers and is considered $s=1 nm$. When graphene is thick, the dielectric definition model type is typically utilized. The surface current model type is generally used when graphene is considered a two-dimensional structure.In general, the 2D conductive surface model for graphene in the device simulation fully and effectively displays its material performance [34].
The biggest obstacles to developing graphene-based electronics are the complex industrial processes and high production costs limiting graphene-based fabrications.
Chemical vapour deposition (CVD) technology is one of the numerous production methods that can efficiently generate graphene on a big scale. The electrical properties of graphene for metasurface or metamaterial-graphene-based structures could decrease due to this method, though.
Pulsed laser deposition (PLD), among other contemporary innovations and techniques, has recently been suggested as a solution to this problem [35–37].
An essential part of THz communication systems is the use of antennas. By adapting antennas to environmental conditions and offering the additional capability for transmitting or receiving data, antenna adjustability can improve their functionality [17,38].
Switches (PIN diodes, FETs), variable reactive loading, and structural modifications are only a few of the devices that can be utilized to modify the operation of antennas [23,24,39]. However, these techniques have disadvantages, including the rapid tuning speed in PIN diodes or the restricted dynamic range in variable reactive loading. Graphene can be used with metamaterials and metasurfaces to give a significant bandwidth, illumination direction, and polarization reconfigurability. These structures produce orbital angular momentum waves, among other uses for graphene-based metamaterials besides antenna layout [38,40].
Figure 3 shows the geometry of the graphene-based array patch antenna, which consists of the microstrip feed and the octagonal patch.
All the parameters are optimized to achieve the best results. The dimension of the proposed array antenna is illustrated in Table 1.
Table 1. Dimension of the proposed array antenna structure.
This antenna is developed using graphene with the specifications of $\tau = 1.6 ps$, $T = 300 k$, and $E_f = 2.2 eV$ on a substrate with a relative permittivity of 2.2 and a thickness of $50 \mu m$. To design the array square patch antenna, the following equation is used [41–43]:
Then, a little triangular shape is created in each microstrip patch antenna’s four beam angles. We achieve an octagonal patch antenna in the THz band in this method. A small transition microstrip line connects the patches to the feed line to have good impedance matching and decrease the reflection coefficient [44].
The results of the return loss are simulated by using CST Microwave Studio. A waveguide port is used to excite the graphene octagonal patch antenna. The surface impedance $Z_s$ connects the electric field’s tangential component and the interface’s surface current.
The surface current created on the graphene surface is correlated with the surface conductivity $\sigma _s$ and the tangential component of the electric field.
The boundary conditions at the graphene interface can be defined as [45,46]
Although the intraband contribution dominates in the frequency range of interest (0.3 to 3 THz) [45,47,48], the graphene patch’s overall conductivity will be entirely intraband.
Where $Z_s$=1/$\sigma$ is the surface impedance of the graphene sheet, the boundary conditions can be used to determine the electromagnetic problems, which can be simply solved with less computational cost.
Figure 4 shows the simulated transmission coefficient parameters ($|S_{21}|$ and $|S_{12}|$) within the same low THz frequency band of reflection coefficient parameters. It can be inferred from the results that antenna matching occurs in ideal situations in the frequency range of 0.620 to 0.928 THz. Both values are less than 10 dB as the general rule ($|S_{21}|$ and $|S_{12}|$ < -10 dB) with a bandwidth of 308 GHz.
Fig. 4. Simulation results of transmission and reflection coefficients related to the proposed antenna.
The directivity plot at each frequency over the -10 dB impedance matching bandwidth (600-900 GHz) is shown in Fig. 5.
It is important to note that the antenna’s directivity remains approximately constant over the operational bandwidth. The E-field distribution for reconfigurable graphene-based microstrip patch antenna in the central frequency of 0.7 THz is shown in Fig. 6.
It is observed that the maximum electric field is $1.30 \times 10^{6}$ $V/m$ at the resonating frequency of 0.7 THz. It is important to note that there is a significant amplification in the field strength of the graphene patch antenna, which makes a notable difference between the radio frequency antenna and the graphene antenna in the THz band.
5. Beam pattern control
As shown in Fig. 7, modulated pulses with central frequencies of 660 GHz and 740 GHz are amplified about 22.6 dB by passing through 45 km fiber ($\beta _2$=-0.0059 $ps^2/km$) under MI and placing on the sideband of the carrier with the Power and frequency of P=300 mW and f=193 THz, respectively.
To achieve high gain, it needs to increase the length of the fiber. It is essential to mention that due to the small amount of nonlinear index of refraction of the fiber ($n_2$= $10^{-20}$ $m^{2}.W^{-1}$), signal distortion does not occur for less than 75 km fiber length.
Then, the desired time delay is tuned by changing the fiber length used in the bit-control system. The dispersion matrix is built around a binary delay line of optical switch devices and dispersive fibers (three bits are illustrated in Fig. 1). We use a thread with positive dispersion fiber ($\beta _2>0$) in the control system to decrease the time delay achieved due to fibre under MI.
The pattern of PAA for the state without time delay and times delay of 0.12 ps, 0.24 ps, and 0.36 ps is shown in Fig. 8. According to the mentioned time delays, the figures show antenna patterns in angles of $6^\circ$, $12^\circ$, and $18^\circ$. The minimum time delay can be determined based on the dispersion and the minimum fiber length used in the control system.
Fig. 8. normalization pattern in angles of $0^\circ$, $6^\circ$, $12^\circ$, and $18^\circ$ with respect to binary-code in bit-control system.
6. Conclusion
In this article, we proposed a novel and simple system for improving the $V_{\pi }$ of the MZM, creating a spontaneous gain, and controlling the beam pattern for an array antenna at the THz band. The suggested RoF system, using 60 km fiber under MI, achieves 32 dB gain and over 40 times reduction in $V_{\pi }$. This technique can be implemented for various time delays using a control system based on changing fiber length to create different PAA’s beam patterns. So the pattern is shown by selecting minimum time delays of 0.12 ps for creating beam-angles of $6^\circ$, $12^\circ$, and $18^\circ$ with respect to binary code in the bit-control system.
In this case, it is used a special design of two elements graphene-based array patch antenna that covers an acceptable bandwidth range that operates over the lower THz frequency band of 620–928 GHz, providing a bandwidth of 308 GHz with a return loss of almost 31 dB at the center frequency of 700 GHz.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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